Planetary Astronomyweek 1

PHYS 1051 Dr. Jason Pinkney

Goals for this course1) Obtain knowledge about astronomy.

2) Obtain understanding of some basic physics concepts.

3) Get practice and gain confidence in problem solving and math.

4) Learn about science and how it differs from pseudosciences and other belief systems.

5) Expand your personal “theory of everything” - your cosmology.

Week 1 of Stellar and Galactic Astronomy

View the film “Powers of 10 A Film About the Relative Sizes of Things 1977

by Charles and Ray EamesNarrated by Phillip Morrison

Pre-Questions1) Note the largest scale achieved.2) Note the smallest scale achieved.3) In which powers of 10 do we find great “voids” where nothing new enters the view?

Also consider ...4) In every 10 seconds, the view expands by a factor of 10. Could this entire journey be experienced while flying in a rocket ship?

Why do we need powers of 10?Why do we need powers of 10? Many quantities have a vast range of values Many quantities have a vast range of values in Astronomy ...in Astronomy ...

1) Distances. 10-16 to 1024 meters (actually >1026) for the scale of an atomic nucleus compared to the scale of largest structures in the universe.

2) Time. 10-46 second to 1016 seconds (109 yrs) for the Planck time to the age of the universe.

3) Masses: 10-31 kg (electrons) to 1045 kg (clusters of galaxies)

4) Energies: and 10-19 Joules for H-alpha photon to 10+39 Joules for Gamma-Ray Bursts.

5) Speeds: continental drift (cm/yr) to the speed of light 300,000,000 m/s.

Without powers of 10: 1024 = 1,000,000,000,000,000,000,000,000

And that's why we use “powers of 10” -- to make them more manageable!

Understanding Powers of 10, orders of magnitude, and Scientific Notation

Scientific Notation: a way of writing a number in which the decimal pointIs placed to the right of the most significant digit, and this is multipliedby 10P where P=an integer (the exponent, or “power of 10”)Exponential Notation Format: Coefficient X Base exponent

(where Base=10) Example: 58400 = 5.84X104

Example: 0.01093 = 1.093x10-2

Example: The average Earth-Sun distance is 93,000,000 miles or 9.3107 miles.

Power of 10: one can approximate a number by giving only the exponent ofthat number expressed in scientific notation, rounded up or down dependingon the coefficient. Example: 5.84x104 = 104.7664 ~ 105 = 10x10x10x10x10 = 100,000. Example of usage: The distance to the Sun from the Earth is about 108 miles. Thus, the Earth-Sun distance is 8 powers of 10 greater than a mile.

Order of magnitude: the "order of magnitude” of a number is the same thing as a number's “power of ten”, it is just used differently in sentences.

Example: “The Earth-Sun distance is 8 orders of magnitude larger than a mile.”)Example: “If you thought the US population was 3 million, you were off by2 orders of magnitude.”

Understanding Powers of 10, orders of magnitude, and Scientific Notation

Rounding to the nearest power of 10.

Previous example: 5.84x104 = 104.7664 ~ 105. But what if we had …Example: 4.84x104 = 104.6848 ~ 105. Example: 3.84x104 = 104.5843 ~ 105. Perhaps if the exponent dropped below 4.5 …Example: 2.84x104 = 104.4533 ~ 104. Finally, we don't round up!

For which coefficient will the exponent be exactly 4.5? Answer: 3.162278 (=√10)

Example: 3.1623x104 ~ 105. Example: 3.1622x104 ~ 104.

Try these:

Example: 9.99x102 Example: 9.9x10-2 Example: 5.1x10-4 Example: 3.10x106 Example: 3.20x109

Example: 401,000Example: 301,000Example: 73,162,055,319

~ 103

~ 10-1. ~ 10-3. ~ 106. ~ 1010.

~ 106.~ 105.~ 1011.

Why do we need powers of 10?Why do we need powers of 10?

1) To compress long numbers. Example: mass of the Sun in kilograms:

1 M⊙ = 2.01030 kg (sci notation)1 M⊙ =1030 kg (nearest power of 10)

(Now try writing this number as a 1 with 30 zeros!)

2) To simplify multiplication and division. Example: if the Earth's mass is 1024 kg, how many Earth masses go into

the Sun? M⊙/M = 1030 1024 = 1030-24 = 106

Example: if there are 86400 seconds per day, and 365 days in a year, roughly how many seconds are in a year?

105 * 102 = 105+2 = 107

Simplified multiplication and division allows easy rough estimates called “order of magnitude calculations” or “back of the envelope calculations”. Summary:

With powers of 10, division becomes subtraction and multiplication becomes addition.

Other ways to make large numbers manageable

1) Use prefixes small: deci, centi, milli, micro, nano, pico, femto, atto, zepto, yocto 10 to the: -1 -2 -3 -6 -9 -12 -15 -18 -21 -24

large: deka, hekto, kilo, mega, giga, tera, peta, exa, zeta, yotta 10 to the: 1 2 3 6 9 12 15 18 21 24

Example) What is a convenient unit for 10-6 seconds? Ans: a microsecond (1 μs).

2) Invent new units In astronomy we have ... (red ones are new units) a) The “solar mass”, 1 M⊙ = 2x10^30 kg b) The “astronomical unit”, 1 AU = 1.5x10^8 km, 93,000,000 miles. The average distance between the Earth and Sun. c) The Light year, 1 LY = 9.5 x 10^12 km The distance light travels through space in a year. Good for distances between stars. d) The parsec, 1 pc = 3.1 x 10^13 km. The distance one must be from the Solar system so that the Earth-Sun separation appears to be 1 arcsecond. Good for distances between stars. e) The kiloparsec, 1 kpc = 1000 pc Good for distances inside a galaxy f) The megaparsec, 1 Mpc = 1,000,000 pc Good for distances between galaxies, clusters, superclusters.

Side notes on astronomical distances / sizes

1) The magic number, 110.

110 (roughly) comes up many times in distance ratios. 110 = DiamSun/DiamE = distSun/DiamSun = distMoon/DiamMoon

2) The AU and Light Year. There are 63,000 AU in 1 LY. Coincidentally, there are 63,000 inches in a mile!

3) The distance to the Moon is 240,000 miles. A good car typically lasts about 240,000 miles. So you might be able to drive to the Moon if there were a direct route from Earth!

4) The ratio 400. 400 = DistSun/distMoon = DiamSun/diamMoon Because of this coincidence the Sun and Moon subtend about the same angle in the sky (½ degree) and we can observe both total and annular solar eclipses.

Things that we can see with the naked eye

1. Sun2. Moon3. 5 planets (+Uranus, just visible)4. 6500 stars (down to +6.0 mag)5. 3 galaxies (M31,LMC,SMC. Some can see M33)6. Comets7. Supernovae, novae8. Meteors (in our atmosphere)9. Aurora (in our atmosphere)

The Naked – Eye Universe

The Top Ten Brightest Objects in the Sky

1. Sun2. Moon3. Venus4. Mars5. Jupiter6. Mercury7. Sirius8. Saturn9. Canopus (in Carina, Southern Hem)10. Alpha Centauri (Rigel Kentaurus)

Arcturus, Vega, and Capella are almost a tie for 11th!

The Naked – Eye Universe (FAST)

Constellations and Asterisms

Constellation: a designated region in the sky containing one or morehistorical star patterns. Demarcations by the IAU.

Asterism: a recognizable pattern of stars.

Ex) OrionEx) Ursa MajorEx) Taurus

* 88 total constellations* More than 88 asterisms* Northern constellations named after Greek Mythological characters

The Naked – Eye Universe

Example:Orion.

An easily recognizedconstellation!

Try a planetarium program like “Stellarium” to see the sky in motion.